Related papers: Mean Gradient Descent: An optimization approach fo…
Diffusion models have shown remarkable flexibility for solving inverse problems without task-specific retraining. However, existing approaches such as Manifold Preserving Guided Diffusion (MPGD) apply only a single gradient update per…
Lensless in-line holography is a simple, portable, and cost-effective method of imaging especially for the biomedical microscopy applications. We propose a multiplicative gradient descent optimization based method to obtain multi-depth…
Under mild assumptions stochastic gradient methods asymptotically achieve an optimal rate of convergence if the arithmetic mean of all iterates is returned as an approximate optimal solution. However, in the absence of stochastic noise, the…
Stochastic gradient descent (SGD) is a simple and popular method to solve stochastic optimization problems which arise in machine learning. For strongly convex problems, its convergence rate was known to be O(\log(T)/T), by running SGD for…
Optimization problem, which is aimed at finding the global minimal value of a given cost function, is one of the central problem in science and engineering. Various numerical methods have been proposed to solve this problem, among which the…
Gradient Descent (GD) is a ubiquitous algorithm for finding the optimal solution to an optimization problem. For reduced computational complexity, the optimal solution $\mathrm{x^*}$ of the optimization problem must be attained in a minimum…
The stochastic gradient descent (SGD) optimization algorithm plays a central role in a series of machine learning applications. The scientific literature provides a vast amount of upper error bounds for the SGD method. Much less attention…
Inspired by the recent advances on minimizing nonsmooth or bound-constrained convex functions on models using varying degrees of fidelity, we propose a line search multigrid (MG) method for full-wave iterative image reconstruction in…
Regularization is a widely recognized technique in mathematical optimization. It can be used to smooth out objective functions, refine the feasible solution set, or prevent overfitting in machine learning models. Due to its simplicity and…
The low-rank matrix recovery problem seeks to reconstruct an unknown $n_1 \times n_2$ rank-$r$ matrix from $m$ linear measurements, where $m\ll n_1n_2$. This problem has been extensively studied over the past few decades, leading to a…
Sampling from an unnormalized target distribution is an essential problem with many applications in probabilistic inference. Stein Variational Gradient Descent (SVGD) has been shown to be a powerful method that iteratively updates a set of…
Stochastic gradient descent (SGD) method is popular for solving non-convex optimization problems in machine learning. This work investigates SGD from a viewpoint of graduated optimization, which is a widely applied approach for non-convex…
We study the inverse problem of radiative transfer equation (RTE) using stochastic gradient descent method (SGD) in this paper. Mathematically, optical tomography amounts to recovering the optical parameters in RTE using the…
Stochastic Gradient Decent (SGD) is one of the core techniques behind the success of deep neural networks. The gradient provides information on the direction in which a function has the steepest rate of change. The main problem with basic…
In this paper, we design unimodular waveforms with good correlation properties for multi-input multi-output (MIMO) radar systems. Specifically, first, we analyze the geometric properties of the unimodular constraint in the fourth-order…
In this paper, we study the minimax optimization problem in the smooth and strongly convex-strongly concave setting when we have access to noisy estimates of gradients. In particular, we first analyze the stochastic Gradient Descent Ascent…
Low-rank matrix estimation is a canonical problem that finds numerous applications in signal processing, machine learning and imaging science. A popular approach in practice is to factorize the matrix into two compact low-rank factors, and…
We present the Multilevel Bregman Proximal Gradient Descent (ML BPGD) method, a novel multilevel optimization framework tailored to constrained convex problems with relative Lipschitz smoothness. Our approach extends the classical…
Minimax optimal convergence rates for classes of stochastic convex optimization problems are well characterized, where the majority of results utilize iterate averaged stochastic gradient descent (SGD) with polynomially decaying step sizes.…
We propose a new stochastic optimization framework for empirical risk minimization problems such as those that arise in machine learning. The traditional approaches, such as (mini-batch) stochastic gradient descent (SGD), utilize an…